Mathematics, 22.02.2022 14:00 prettyprincess9643
You want to set up a retirement account. You are going to put $25,000 into the account. How
long will it take for each account to double in value.
1) An account offering 5.3% interest per year
compounded quarterly.
2) An account offering 7.2% interest per year
compounded monthly.
Answers: 1
![50000=25000\left(1+\frac{0.053}{4}\right)^{4\cdot t}\implies \cfrac{50000}{25000}=(1.01325)^{4t}\implies 2=(1.01325)^{4t} \\\\\\ \log(2)=\log[(1.01325)^{4t}]\implies \log(2)=t\log(1.01325^4) \\\\\\ \cfrac{\log(2)}{\log(1.01325^4)}=t\implies 13\approx t \\\\[-0.35em] ~\dotfill](/tpl/images/2667/1835/d5515.png)
![50000=25000\left(1+\frac{0.072}{12}\right)^{12\cdot t}\implies \cfrac{50000}{25000}=(1.006)^{12t}\implies 2=(1.006)^{12t} \\\\\\ \log(2)=\log[(1.006)^{12t}]\implies \log(2)=t\log(1.006^{12}) \\\\\\ \cfrac{\log(2)}{\log(1.006^{12})}=t\implies \stackrel{\textit{about 9 years and 252 days }}{9.7\approx t}](/tpl/images/2667/1835/ef6f5.png)
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